Question 1

Suppose the probability is 0.65 that the stock market will increase in value during a given year (event A). The probability that a financial newsletter predicts an increase in the stock market for a year is $$P(B|A) = 0.8 if $$the market actually increases, and $$P(B|A^c) = 0.42 if $$the market decreases. What is the probability that the newsletter predicts an increase in the stock market value during the next year?

Accepted Answer

$$0.667$$

Question 2

A change was proposed in the mathematics curriculum at a college. Math majors were asked whether they approved of the change. Of the 31 females, 10 had no opinion. What percent of the females had no opinion?

Accepted Answer

$$32.26\%$$

Question 3

If $$P(A) = 0.50$$ and $$P(B) = 0.40$$, what is $$P(A 	ext{ or } B) if A $$and B are independent?

Accepted Answer

$$0.70$$

Question 4

In a survey, 32% of adult males had high cholesterol (event A), 27% had high blood pressure (event B), and 52% had neither. What is the probability an adult male has high cholesterol and high blood pressure?

Accepted Answer

$$0.11$$

Question 5

Given that a male has high blood pressure, what is the probability he has high cholesterol? ($$P(A|B))$$

Accepted Answer

$$0.4074$$

Question 6

In automotive repair, a rough-running engine can be attributed to bad ignition wires 35% of the time, bad spark plugs 80% of the time, and both problems 20% of the time. Given that the spark plugs are bad, what is the probability that the wires are bad?

Accepted Answer

$$0.25$$

Question 7

If two events are mutually exclusive then they are also independent.

Accepted Answer

B. False

Question 8

Which of the following is NOT a binomial model?

Accepted Answer

A. On your way to university you pass 10 traffic lights. For each traffic light you estimate the probability that it is green to be 0.3. X is the number of times you have to stop at a traffic light.

Question 9

A local school newspaper stated that 97% of San Diego college students oppose the ban of alcohol on Pacific Beach. Suppose we randomly select 15 students. Which statement below is incorrect?

Accepted Answer

C. There are more than two outcomes, so we cannot apply the binomial formula.

Question 10

Markus estimates the probability of catching no waves is 0.1, one wave is 0.1, two waves is 0.2, and four or more waves is 0.4. What is the probability that Markus will catch 3 waves?

Accepted Answer

$$0.3$$

Question 11

Thirty-four percent of workers in the United States are college graduates. Suppose a random sample of 120 workers is obtained. What are the mean and standard deviation of the number of workers with a college degree, respectively?

Accepted Answer

$$40.8$$ and $$5.1892$$

Question 12

Scores on a standardized test are normally distributed with a standard deviation of 25. Suppose David scored a 245 on the test and that placed him on the 84th percentile. What was the mean score?

Accepted Answer

$$220$$

Question 13

Assuming that the weekly food expenditures of families of a certain size in one economic group are approximately normally distributed with a mean of $$145$$ and a standard deviation of $$22. $$What is the value of the first quartile for this distribution?

Accepted Answer

$$130.26$$

Question 14

According to the Air Transport Association of America, the average operating cost of an MD-80 jet airliner is $$2087$$ per hour with a standard deviation of $$175. $$What is the probability that a randomly selected MD-80 jet airliner costs more than $$2500$$ per hour to operate?

Accepted Answer

$$0.0091$$

Question 15

A consumer organization inspecting new cars found that 61% had no defects, 21% had one defect, 11% had two defects and 7% had three defects. What is the expected number of defects in a new car?

Accepted Answer

$$0.64$$

Question 16

The length of a newborn harbor seal follows a normal distribution with a mean length of $$29.5$$ inches and standard deviation $$1.2$$ inches. What is the probability that a randomly selected newborn seal is less than $$27$$ inches long?

Accepted Answer

$$0.0188$$

Question 17

In Mexico, 70% of drivers who are arrested for DWI are convicted. Suppose 15 independently selected drivers are arrested for DWI. What is the probability that at least 14 of the 15 drivers are convicted?

Accepted Answer

$$0.0305$$

Question 18

According to the State Department, only 27% of Americans carry a valid passport. Suppose we take a random sample of 11 Americans. Which of the following best describes the distribution of $$X=$$ number of Americans that carry a valid passport?

Accepted Answer

$$X \sim B(11, 0.27)$$

Question 19

The gas mileage for a new model of car is normally distributed, with a standard deviation of $$3.5$$ mpg. If only 4% of the cars have a gas mileage of less than $$20$$ mpg, what is the mean of the distribution?

Accepted Answer

$$26.125$$

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